LInear vs Nonlinear

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What characterizes a linear function?

Back

A linear function is characterized by a constant rate of change, meaning it produces a straight line when graphed.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not have a constant rate of change and produces a curve when graphed.

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant difference in the y-values for equal intervals in the x-values.

Front

What does it mean if a set of coordinates represents a nonlinear function?

Back

It means that the relationship between the x and y values does not produce a straight line when graphed.

Front

What is the slope in a linear equation?

Back

The slope is the measure of the steepness of the line, represented by 'm' in the equation y = mx + b.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by 'b' in the equation y = mx + b.

Front

Can a linear function have a negative slope?

Back

Yes, a linear function can have a negative slope, which means the line goes down as it moves from left to right.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2, which produces a parabolic curve when graphed.

Front

What does it mean for a function to be 'not a function'?

Back

A relation is 'not a function' if any x-value is associated with more than one y-value.